Electroabsorption in Semiconductors: The Excitonic Absorption Edge

Abstract

Numerical calculations of the optical-absorption coefficient for direct, excitonic transitions in a uniform applied electric field are presented. The electron-hole scattering is treated within the effective-mass approximation and leads to an absorption coefficient which differs markedly in size and shape from the Franz-Keldysh absorption spectrum. A detailed numerical study of the shape of the absorption-edge spectrum at photon energies somewhat below the zero-field absorption threshold suggests that for small field strengths the dominant asymptotic form of the absorption coefficient is $\mathrm{exp}(\ensuremath{-}\frac{{C}_{0}|E\ensuremath{-}{{E}_{0}}^{\ensuremath{'}}|}{f})$, where $f=\frac{|e|\mathrm{Fa}}{R}$ is the electric field strength in units of exciton Rydbergs per electron-exciton Bohr radius. This result contradicts the existing belief that the electron-hole interaction does not alter the asymptotic form of the Franz-Keldysh shape: $\mathrm{exp}(\ensuremath{-}\frac{{{C}_{0}}^{\ensuremath{'}}{|E\ensuremath{-}{{E}_{0}}^{\ensuremath{'}}|}^{\frac{3}{2}}}{f})$. Physical arguments are presented to show why the exciton effects should be important. A discussion is presented of the interrelationships among the present treatment of electro-absorption and various one-electron, exciton, and many-body formalisms.